Abstract

We describe plasmon propagation in silica-filled coupled nanovoids fully buried in gold. Propagation bands and band gaps are shown to be tunable through the degree of overlap and plasmon hybridization between contiguous voids. The effect of disorder and fabrication imperfections is thoroughly investigated. Our work explores a novel paradigm for plasmon photonics relying on plasmon modes in metal-buried structures, which can benefit from long propagation distances, cancelation of radiative losses, minimum crosstalk between neighboring waveguides, and maximum optical integration in three-dimensional arrangements.

©2009 Optical Society of America

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References

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  8. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006).
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    [Crossref]
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    [Crossref]
  29. I. Romero, T. V. Teperik, and F. J. García de Abajo, “Plasmon molecules in overlapping nanovoids,” Phys. Rev. B 77, 125,403 (2008).
    [Crossref]
  30. R.M. Cole, J. J. Baumberg, F. J. García de Abajo, S. Mahajan, M. Abdelsalam, and P. N. Bartlett, “Understanding plasmons in nanoscale voids,” Nano Lett. 7, 2094–2100 (2007).
    [Crossref]
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    [Crossref] [PubMed]
  32. I. Romero, J. Aizpurua, G.W. Bryant, and F. J. García de Abajo, “Plasmons in nearly touching metallic nanoparticles: Singular response in the limit of touching dimers,” Opt. Express 14, 9988–9999 (2006).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  36. F. Ouyang and M. Isaacson, “Surface plasmon excitation of objects with arbitrary shape and dielectric constant,” Philos. Mag. B 60, 481–492 (1989).
    [Crossref]
  37. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [Crossref]
  38. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Harcourt College Publishers, New York, 1976).

2009 (2)

A. Manjavacas and F. J. García de Abajo, “Robust plasmon waveguides in strongly interacting nanowire arrays,” Nano Lett. 9, 1285–1289 (2009).
[Crossref]

X. V. Li, R. M. Cole, C. A. Milhano, P. N. Bartlett, B. F. Soares, J. J. Baumberg, and C. H. de Groot, “The fabrication of plasmonic Au nanovoid trench arrays by guided self-assembly,” Nanotech. 20, 285,309 (2009).
[Crossref]

2008 (6)

M. Tymczenko, L. F. Marsal, T. Trifonov, I. Rodriguez, F. Ramiro-Manzano, J. Pallares, A. Rodriguez, R. Alcubilla, and F. Meseguer, “Colloidal crystal wires,” Adv. Mater. 20, 2315–2318 (2008).
[Crossref]

I. Romero, T. V. Teperik, and F. J. García de Abajo, “Plasmon molecules in overlapping nanovoids,” Phys. Rev. B 77, 125,403 (2008).
[Crossref]

F. J. García de Abajo and M. Kociak, “Probing the photonic local density of states with electron energy loss spectroscopy,” Phys. Rev. Lett. 100, 106,804 (2008).
[Crossref]

V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. García de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37, 1792–1805 (2008).
[Crossref] [PubMed]

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100, 023,901 (2008).
[Crossref]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for sub-wavelength confinement and long-range propagation,” Nat. Phot. 2, 496–500 (2008).
[Crossref]

2007 (4)

A. F. Koenderink, R. deWaele, J. C. Prangsma, and A. Polman, “Experimental evidence for large dynamic effects on the plasmon dispersion of subwavelength metal nanoparticle waveguides,” Phys. Rev. B,  76, 201403 (2007).
[Crossref]

R.M. Cole, J. J. Baumberg, F. J. García de Abajo, S. Mahajan, M. Abdelsalam, and P. N. Bartlett, “Understanding plasmons in nanoscale voids,” Nano Lett. 7, 2094–2100 (2007).
[Crossref]

T. D. Onuta, M. Waegele, C. C. DuFort, W. L. Schaich, and B. Dragnea, “Optical field enhancement at cusps between adjacent nanoapertures,” Nano Lett. 7, 557–564 (2007).
[Crossref] [PubMed]

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316, 430–432 (2007).
[Crossref] [PubMed]

2006 (8)

J. J. Baumberg, “Breaking the mould: Casting on the nanometre scale,” Nat. Mater. 5, 2–5 (2006).
[Crossref]

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74, 033402 (2006).
[Crossref]

G. Gantzounis and N. Stefanou, “Cavity-plasmon waveguides: Multiple scattering calculations of dispersion in weakly coupled dielectric nanocavities in a metallic host material,” Phys. Rev. B 74, 085,102 (2006).
[Crossref]

I. Romero, J. Aizpurua, G.W. Bryant, and F. J. García de Abajo, “Plasmons in nearly touching metallic nanoparticles: Singular response in the limit of touching dimers,” Opt. Express 14, 9988–9999 (2006).
[Crossref] [PubMed]

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96, 097,401 (2006).
[Crossref]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006).
[Crossref] [PubMed]

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: The next chip-scale technology,”Mater. Today 9, 20–27 (2006).
[Crossref]

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[Crossref] [PubMed]

2005 (1)

T. A. Kelf, Y. Sugawara, J. J. Baumberg, M. Abdelsalam, and P. N. Bartlett, “Plasmonic band gaps and trapped plasmons on nanostructured metal surfaces,” Phys. Rev. Lett. 95, 116,802 (2005).
[Crossref]

2004 (1)

L. A. Blanco and F. J. García de Abajo, “Spontaneous light emission in complex nanostructures,” Phys. Rev. B 69, 205,414 (2004).
[Crossref]

2003 (2)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
[Crossref] [PubMed]

2001 (4)

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of asymmetric structures,” Phys. Rev. B 63, 125,417 (2001).
[Crossref]

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, “Plasmonics - a route to nanoscale optical devices,” Adv. Mater. 13, 1501–1505 (2001).
[Crossref]

S. I. Bozhevolnyi, J. Erland, K. Leosson, P.M.W. Skovgaard, and J.M. Hvam, “Waveguiding in surface plasmon polariton band gap structures,” Phys. Rev. Lett. 86, 3008–3011 (2001).
[Crossref] [PubMed]

S. Coyle, M. C. Netti, J. J. Baumberg, M. A. Ghanem, P. R. Birkin, P. N. Bartlett, and D.M. Whittaker, “Confined plasmons in metallic nanocavities,” Phys. Rev. Lett. 87, 176,801 (2001).
[Crossref]

2000 (1)

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B 61, 10,484–10,503 (2000).
[Crossref]

1999 (1)

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
[Crossref]

1998 (1)

1997 (1)

F. J. García de Abajo and J. Aizpurua, “Numerical simulation of electron energy loss near inhomogeneous dielectrics,” Phys. Rev. B 56, 15,873–15,884 (1997).
[Crossref]

1996 (1)

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “Full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
[Crossref] [PubMed]

1989 (1)

F. Ouyang and M. Isaacson, “Surface plasmon excitation of objects with arbitrary shape and dielectric constant,” Philos. Mag. B 60, 481–492 (1989).
[Crossref]

1981 (1)

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927–1930 (1981).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Abdelsalam, M.

R.M. Cole, J. J. Baumberg, F. J. García de Abajo, S. Mahajan, M. Abdelsalam, and P. N. Bartlett, “Understanding plasmons in nanoscale voids,” Nano Lett. 7, 2094–2100 (2007).
[Crossref]

T. A. Kelf, Y. Sugawara, J. J. Baumberg, M. Abdelsalam, and P. N. Bartlett, “Plasmonic band gaps and trapped plasmons on nanostructured metal surfaces,” Phys. Rev. Lett. 95, 116,802 (2005).
[Crossref]

Aizpurua, J.

I. Romero, J. Aizpurua, G.W. Bryant, and F. J. García de Abajo, “Plasmons in nearly touching metallic nanoparticles: Singular response in the limit of touching dimers,” Opt. Express 14, 9988–9999 (2006).
[Crossref] [PubMed]

F. J. García de Abajo and J. Aizpurua, “Numerical simulation of electron energy loss near inhomogeneous dielectrics,” Phys. Rev. B 56, 15,873–15,884 (1997).
[Crossref]

Alcubilla, R.

M. Tymczenko, L. F. Marsal, T. Trifonov, I. Rodriguez, F. Ramiro-Manzano, J. Pallares, A. Rodriguez, R. Alcubilla, and F. Meseguer, “Colloidal crystal wires,” Adv. Mater. 20, 2315–2318 (2008).
[Crossref]

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Harcourt College Publishers, New York, 1976).

Atwater, H. A.

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316, 430–432 (2007).
[Crossref] [PubMed]

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
[Crossref] [PubMed]

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, “Plasmonics - a route to nanoscale optical devices,” Adv. Mater. 13, 1501–1505 (2001).
[Crossref]

Aussenegg, F. R.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
[Crossref]

M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, “Electromagnetic energy transport via linear chains of silver nanoparticles,” Opt. Lett. 23, 1331–1333 (1998).
[Crossref]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

S. C. Kitson, W. L. Barnes, and J. R. Sambles, “Full photonic band gap for surface modes in the visible,” Phys. Rev. Lett. 77, 2670–2673 (1996).
[Crossref] [PubMed]

Bartlett, P. N.

X. V. Li, R. M. Cole, C. A. Milhano, P. N. Bartlett, B. F. Soares, J. J. Baumberg, and C. H. de Groot, “The fabrication of plasmonic Au nanovoid trench arrays by guided self-assembly,” Nanotech. 20, 285,309 (2009).
[Crossref]

R.M. Cole, J. J. Baumberg, F. J. García de Abajo, S. Mahajan, M. Abdelsalam, and P. N. Bartlett, “Understanding plasmons in nanoscale voids,” Nano Lett. 7, 2094–2100 (2007).
[Crossref]

T. A. Kelf, Y. Sugawara, J. J. Baumberg, M. Abdelsalam, and P. N. Bartlett, “Plasmonic band gaps and trapped plasmons on nanostructured metal surfaces,” Phys. Rev. Lett. 95, 116,802 (2005).
[Crossref]

S. Coyle, M. C. Netti, J. J. Baumberg, M. A. Ghanem, P. R. Birkin, P. N. Bartlett, and D.M. Whittaker, “Confined plasmons in metallic nanocavities,” Phys. Rev. Lett. 87, 176,801 (2001).
[Crossref]

Baumberg, J. J.

X. V. Li, R. M. Cole, C. A. Milhano, P. N. Bartlett, B. F. Soares, J. J. Baumberg, and C. H. de Groot, “The fabrication of plasmonic Au nanovoid trench arrays by guided self-assembly,” Nanotech. 20, 285,309 (2009).
[Crossref]

R.M. Cole, J. J. Baumberg, F. J. García de Abajo, S. Mahajan, M. Abdelsalam, and P. N. Bartlett, “Understanding plasmons in nanoscale voids,” Nano Lett. 7, 2094–2100 (2007).
[Crossref]

J. J. Baumberg, “Breaking the mould: Casting on the nanometre scale,” Nat. Mater. 5, 2–5 (2006).
[Crossref]

T. A. Kelf, Y. Sugawara, J. J. Baumberg, M. Abdelsalam, and P. N. Bartlett, “Plasmonic band gaps and trapped plasmons on nanostructured metal surfaces,” Phys. Rev. Lett. 95, 116,802 (2005).
[Crossref]

S. Coyle, M. C. Netti, J. J. Baumberg, M. A. Ghanem, P. R. Birkin, P. N. Bartlett, and D.M. Whittaker, “Confined plasmons in metallic nanocavities,” Phys. Rev. Lett. 87, 176,801 (2001).
[Crossref]

Berini, P.

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of asymmetric structures,” Phys. Rev. B 63, 125,417 (2001).
[Crossref]

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B 61, 10,484–10,503 (2000).
[Crossref]

Birkin, P. R.

S. Coyle, M. C. Netti, J. J. Baumberg, M. A. Ghanem, P. R. Birkin, P. N. Bartlett, and D.M. Whittaker, “Confined plasmons in metallic nanocavities,” Phys. Rev. Lett. 87, 176,801 (2001).
[Crossref]

Blanco, L. A.

L. A. Blanco and F. J. García de Abajo, “Spontaneous light emission in complex nanostructures,” Phys. Rev. B 69, 205,414 (2004).
[Crossref]

Bourillot, E.

J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
[Crossref]

Bozhevolnyi, S. I.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100, 023,901 (2008).
[Crossref]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006).
[Crossref] [PubMed]

S. I. Bozhevolnyi, J. Erland, K. Leosson, P.M.W. Skovgaard, and J.M. Hvam, “Waveguiding in surface plasmon polariton band gap structures,” Phys. Rev. Lett. 86, 3008–3011 (2001).
[Crossref] [PubMed]

Brongersma, M. L.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: The next chip-scale technology,”Mater. Today 9, 20–27 (2006).
[Crossref]

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, “Plasmonics - a route to nanoscale optical devices,” Adv. Mater. 13, 1501–1505 (2001).
[Crossref]

Bryant, G.W.

Chandran, A.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: The next chip-scale technology,”Mater. Today 9, 20–27 (2006).
[Crossref]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Cole, R. M.

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V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. García de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37, 1792–1805 (2008).
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A. F. Koenderink, R. deWaele, J. C. Prangsma, and A. Polman, “Experimental evidence for large dynamic effects on the plasmon dispersion of subwavelength metal nanoparticle waveguides,” Phys. Rev. B,  76, 201403 (2007).
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A. F. Koenderink, R. deWaele, J. C. Prangsma, and A. Polman, “Experimental evidence for large dynamic effects on the plasmon dispersion of subwavelength metal nanoparticle waveguides,” Phys. Rev. B,  76, 201403 (2007).
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X. V. Li, R. M. Cole, C. A. Milhano, P. N. Bartlett, B. F. Soares, J. J. Baumberg, and C. H. de Groot, “The fabrication of plasmonic Au nanovoid trench arrays by guided self-assembly,” Nanotech. 20, 285,309 (2009).
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Sorger, V. J.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for sub-wavelength confinement and long-range propagation,” Nat. Phot. 2, 496–500 (2008).
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T. A. Kelf, Y. Sugawara, J. J. Baumberg, M. Abdelsalam, and P. N. Bartlett, “Plasmonic band gaps and trapped plasmons on nanostructured metal surfaces,” Phys. Rev. Lett. 95, 116,802 (2005).
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M. Tymczenko, L. F. Marsal, T. Trifonov, I. Rodriguez, F. Ramiro-Manzano, J. Pallares, A. Rodriguez, R. Alcubilla, and F. Meseguer, “Colloidal crystal wires,” Adv. Mater. 20, 2315–2318 (2008).
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Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006).
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T. D. Onuta, M. Waegele, C. C. DuFort, W. L. Schaich, and B. Dragnea, “Optical field enhancement at cusps between adjacent nanoapertures,” Nano Lett. 7, 557–564 (2007).
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J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles,” Phys. Rev. Lett. 82, 2590–2593 (1999).
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R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for sub-wavelength confinement and long-range propagation,” Nat. Phot. 2, 496–500 (2008).
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R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: The next chip-scale technology,”Mater. Today 9, 20–27 (2006).
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Adv. Mater. (2)

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A. Manjavacas and F. J. García de Abajo, “Robust plasmon waveguides in strongly interacting nanowire arrays,” Nano Lett. 9, 1285–1289 (2009).
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Nanotech. (1)

X. V. Li, R. M. Cole, C. A. Milhano, P. N. Bartlett, B. F. Soares, J. J. Baumberg, and C. H. de Groot, “The fabrication of plasmonic Au nanovoid trench arrays by guided self-assembly,” Nanotech. 20, 285,309 (2009).
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Nature (2)

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[Crossref] [PubMed]

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[Crossref]

T. A. Kelf, Y. Sugawara, J. J. Baumberg, M. Abdelsalam, and P. N. Bartlett, “Plasmonic band gaps and trapped plasmons on nanostructured metal surfaces,” Phys. Rev. Lett. 95, 116,802 (2005).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. Evolution of void-dimer plasmon energies with overlap distance d. The plasmons are trapped in silica-filled gold-void dimers. The modes are probed through the photonic local density of states (LDOS) at the center of one of the voids, projected along a direction perpendicular to the dimer axis. The void radius is a=240nm. The electric dipole plasmon of the spherical cavity near 900 nm is recovered in the single-void (full overlap at d=-2a) and separated-voids (d=30nm) limits. The LDOS is normalized to its value in an infinite silica environment, εSiO212 ω2 π2 c3 . A vertical offset has been introduced in consecutive spectra for clarity. The intensity of the induced field produced by a dipole at the center of the left void is shown in the insets for selected separations.
Fig. 2.
Fig. 2. Plasmon mixing and splitting with increasing number of gold voids in a linear chain of overlapping silica-filled cavities of radius a=240nm and overlap distance d=-a. Black curves represent the LDOS projected along a direction perpendicular to the chain axis at the center of the leftmost void, while blue curves correspond to an off-axis position. The LDOS is normalized as explained in Fig. 1. A vertical offset has been introduced in consecutive spectra for clarity. The near-field intensity associated to different spectral features is shown as created by dipoles with the orientation and position shown by double arrows in the color-plot insets.
Fig. 3.
Fig. 3. Plasmon propagation in long silica-filled void chains buried in gold. Two different chains are considered: 16 voids and d=-30nm overlap (left); 30 voids and d=-240nm (right). All voids have the same radius a=240nm. The upper plots (a-h) correspond to excitation by a dipole located at the center of the leftmost cavity and oriented perpendicularly with respect to that axis (m=1 azimuthal symmetry relative to the chain axis). The lower plots (i-p) correspond to excitation by a dipole oriented along the axis (m=0 symmetry). For each chain and polarization, the plot on the left (c,g,k,o) shows the induced electric field intensity along the axis of the array, whereas the dispersion plot on the right (d,h,l,p) is the intensity of the Fourier transform of the field along the axis, represented for wavevectors within the first Brillouin zone of the infinite chain (-π/P < q <π/P, where P=2a+d is the period). Near-field plots are shown for photon energies corresponding to non-propagating modes (a,e,i,m) and near the maximum of a propagating mode (b,f,j,n). The dashed curves in the dispersion plots stand for the plasmons of an infinite cylindrical cavity with the same volume as the void-chain cavity. The blue curves in the m=1 case are obtained from the Bloch-wave expansion explained in the text.
Fig. 4.
Fig. 4. Propagation distance in void chains. The field intensity at the center of the rightmost void in the 30-void waveguide of Fig. 3 (a=-d=240nm) is represented by thin red curves for m=1 (upper plots) and m=0 (lower plots). The same quantity is represented by thin black curves for a 20-void waveguide. The source dipole is placed at the center of the leftmost sphere. The smooth thick curves are made to intersect the average of consecutive maxima and minima in each oscillation of the thin curves. A propagation length (right scale) is determined from the ratio of the average curves for the two void lengths considered [ratio=exp(-L/10a)].
Fig. 5.
Fig. 5. Effect of void disorder on plasmon propagation: real-space analysis. The induced electric field intensity is represented in 10-void chains for an exciting dipole situated in the center of the leftmost void and oriented perpendicular (m=1) or parallel (m=0) to the chain axis. The average void radius is a=240nm in all cases and the overlap is d=-a and d=-60nm, as indicated by labels. The upper row of near-field plots corresponds to perfect chains (Δ=0). Lower rows represent the field in chains with different degrees of disordered in the radius a and overlap d (the maximum random displacement is ±Δ; see labels on the left). Two different chain realizations are considered for each non-vanishing value of Δ. The photon energy is taken to match a propagating mode of the perfect chain: 1.45 eV for d=-60nm and 1.48 eV for d=-240nm.
Fig. 6.
Fig. 6. Effect of void disorder on plasmon propagation: reciprocal-space analysis. The dispersion relation of 10-void chains with average radius a=240nm and overlap d=-60nm is represented for different degrees of disorder in a and d (the maximum random displacement is ±Δ; see upper labels). The plots show the squared modulus of the Fourier transform of the on-axis induced electric-field amplitude for m=1 azimuthal symmetry.

Equations (1)

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ε2(ω)ε1(ω)=δ+1δ1,

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